elimination of spades in wheeled military vehicles using ... · elimination of spades in wheeled...

Elimination of spades in wheeled military vehicles using MR-fluid dampers

Ashkan H. Hosseinlooa, Nader Vahdatib,*, Fook Fah Yapa

aNanyang Technological University, School of Mechanical and Aerospace Engineering, 50 Nanyang Avenue, Singapore 639798, Singapore

bThe Petroleum Institute, Department of Mechanical Engineering, PO Box 2533, Abu Dhabi, UAE

ABSTRACT

Tracked military vehicles were the choice of fighting vehicles due to their heavy fire power, better armor package distribution, better traction, and ability to fire on the move without spades. Many armies are converting to all wheeled vehicles, but one of the drawbacks is the inability to fire on the move without spades. A 2D heave pitch vehicle model for HMMWV has been developed. Simulation results indicate that by the use of MR-fluid dampers with the skyhook controls, it is possible to remove the spades, control chassis vibration, and prevent vehicle lift off during mortar firing, without bursting the tires. Keywords: military vehicles, HMMWV, spade, outrigger, MR-fluid damper, vibration control, skyhook control policy

* Corresponding author: E-mail address: [email protected] Tel.: +971 2 607 5787; Fax: +971 2 607 5200.

Active and Passive Smart Structures and Integrated Systems 2011, edited by Mehrdad N. Ghasemi-Nejhad, Proc. of SPIE Vol. 7977, 797715 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.880601

Proc. of SPIE Vol. 7977 797715-1

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NOMENCLATURE

Symbol Definition recoil force recoil mass rear tire mass front tire mass

mortar-chassis mass chassis mass

mortar mass mortar-chassis mass moment of inertia chassis mass moment of inertia

mortar mass moment of inertia recoil stiffness rear suspension stiffness front suspension stiffness rear tire stiffness front tire stiffness rear horizontal stiffness of chassis front horizontal stiffness of chassis

recoil damping coefficient rear suspension damping coefficient front suspension damping coefficient rear tire damping coefficient front tire damping coefficient rear horizontal damping coefficient of chassis front horizontal damping coefficient of chassis

vehicle wheelbase distance from mortar-chassis centre of gravity to front of the car distance from mortar-chassis centre of gravity to rear of the car horizontal distance from mortar-chassis centre of gravity to mortar connection point to chassis distance from mortar centre of gravity to its connection point to chassis along the barrel distance from chassis centre of gravity to rear of the car distance from chassis centre of gravity to front of the car horizontal distance from chassis centre of gravity to mortar connection point to chassis mortar elevation angle from horizon vertical distance from mortar-chassis centre of gravity to mortar connection point to chassis vertical distance from mortar-chassis centre of gravity to rear suspension vertical distance from mortar-chassis centre of gravity to front suspension vertical distance from chassis centre of gravity to front suspension vertical distance from chassis centre of gravity to rear suspension vertical distance from chassis centre of gravity to mortar connection point to chassis vertical distance from chassis centre of gravity to that of mortar-chassis system



1 INTRODUCTION Many armies are replacing heavy slow tracked vehicles with their lighter wheeled counterparts for their high mobility and better shoot and scoot capabilities. By putting its $40-billion ground combat vehicle (GCV) procurement plan on hold, the U.S. Army is giving itself a breather to come up with a new strategy for its ground vehicle force1. This hold took place because the U.S. army and defense department believe that they should rethink about buying and even developing the tracked vehicles. Many armies, around the world, are moving away from tracked vehicles except for specific missions. “Tracked vehicles are not necessarily the best option for what we plan to be doing,” says John Gresham, a defense analyst and author of several books on military equipment and operations1. Due to their high inertia and rigidity, tracked vehicles are capable of carrying heavy artillery guns and mortars on them and firing them as well without any need for spades or outriggers. However, it will be more mobile and deployable if they are mounted on lighter wheeled vehicles. But a problem with light wheeled vehicles is that they may not be able to tolerate excessive firing force exerted on them by the mortar system if the same heavy and high caliber guns, like those used for heavy tracked vehicles, are used and this problem may manifest itself as vehicle lift-off, flip over, slide, excessive vibration, and tire burst-out. To prevent military wheeled vehicles flip over or from tire burst-out during mortar firing, spades (outriggers) are utilized to connect the vehicle to the ground so as to transmit some of the mortar firing force to the ground. Making use of spades contradicts with the essential philosophy of fast shoot and scoot. Addition of spades to wheeled military vehicles, during mortar fire, makes the vehicle stationary and a target by the enemy fire, reduces the mobility of the vehicle, makes the vehicle heavy thus increasing fuel consumption, and results in considerable time to plant the spades into the ground and retract them after firing. However, if the spades can be eliminated, the vehicle will be more mobile and never stationary, hence hard to track and target by the enemy. This idea is strengthened by advent of new technologies in recoil systems; one of which is Super Rapid Advanced Mortar System (SRAMS) designed and developed by Singapore Technologies with much lower recoil force in comparison to its counterparts. Therefore, research study is conducted in this paper to see if spades can be eliminated by modeling a High Mobility Multi-Purpose Wheeled Vehicle (HMMWV) with a 120 mm gun (SRAMS) on it. To this end, multi-body dynamic model of HMMWV with its mounted 120mm SRAMS is developed and Magneto-Rheological Fluid (MRF) shock absorbers are utilized as the primary suspension to control vehicle response during and after firing. The reason for using MR dampers is that some of military vehicles are already using MR dampers as their primary suspensions and thus it reduces the cost for implementation. The HMMWV math model, control strategy, and simulation results will be discussed and presented in details in this paper.

2 LITERATURE REVIEW Majority of the publications done on modeling, analysis and control of wheeled military vehicles are almost all done only for maneuvering purposes rather than for integrated firing purposes. Only few studies have been carried out for analysis and control of recoil systems of the cannons but not cannons installed on the wheeled vehicles. Since here in this paper, we are dealing with response of military wheeled vehicles to mortar fire, it will be very difficult to find many publications in this area due to the nature of this work being military. Many research studies have been conducted in the first category, i.e. modeling, analysis and control of the wheeled military vehicles. Sleight and Agrawal2 developed a dynamic model for autonomous control of high mobility multipurpose wheeled vehicles. Ersal T. et al3, used their method, namely importance analysis, to obtain a reduced dynamic model for a HMMWV, for ride evaluation. In addition, Grujicic M. et al4 employed Finite-element-based transient non-linear dynamics and multi-body longitudinal dynamics to investigate blast survivability and off-road performance of a HMMWV. Control of these military vehicles for different maneuvering criteria has been quite well studied mostly using semi-active skyhook, ground-hook, and hybrid control strategies and semi-active primary suspensions. Due to drawbacks of active



control, semi-active control is the most widely used control strategy in a broad range of engineering applications as well as in military applications. To this end, Magneto-Rheological (MR) dampers have been commonly employed as the semi-active primary suspension systems. Gordaninejad and Kelso5 employed Bingham plastic theory to model nonlinear behavior of MR fluids to design a MR damper for the primary suspension of a HMMWV. Karakas E. et al6 experimentally investigated and compared the performance of a MR damper with that of an Original Equipment Manufacturer (OEM) damper as mounted in a quarter car test rig (representing a ¼ car HMMWV) suspension. The mathematical model they used was a two degree of freedom model and the control policy utilized was a semi-active skyhook control. A year later, Liu Y. et al7 did an experimental study on fuzzy logic control of a quarter-car-model of a HMMWV suspension system using a magneto-rheological fluid damper and compared it with skyhook method. Although the studies conducted in the first category did not take the integrated firing dynamics into account and their purpose was mainly regarding maneuverability and ride performance, reviewing their vehicle models and control strategies could be useful for the integrated firing purposes and controls in this paper. Works done in the second category i.e. analysis and control of recoil systems of mortars, are also of very significant importance to the vibration control of the vehicles on which the mortars are mounted. A properly designed recoil system for a mortar can significantly reduce the transmitted force felt by the trunnion. Reducing this force enables employing larger caliber guns on military vehicles which can handle higher impulse munitions. Higher impulse guns are necessary for defeating threats at greater distances while reduced transmitted force on trunnion pins allows for lighter vehicles which consequently results in greater mobility, deployability and range. One of the mechanisms used in recoil systems is fire out-of-battery (FOOB) mechanism. This mechanism, known also as soft recoil, can reduce the firing impulses by pre-accelerating (direction opposite of conventional recoil) the recoiling parts before ignition. Ahmadian and Poynor8 studied MR dampers for controlling recoil dynamics. They showed the recoil force increases and the recoil stroke decreases nonlinearly with an increase in the damping force. A year later, Ahmadian M. et al9 did an analytical study on fire out-of-battery recoil systems using MR dampers. They concluded that MR dampers would have quite the same performance in FOOB recoil systems as conventional dampers except they can overcome firing faults of FOOB systems, namely pre-fire, hang-fire and misfire, to a good extent. This work was followed by their experimental work10, with the use of electrothermal-chemical ignition in conjunction with a fire out-of-battery recoil system that showed if it is not possible practically to eliminate the occurrence of a FOOB firing fault modes, it can be reduced significantly. Hu H. et al11 tried to find an accurate nonlinear model for a recoil system equipped with MR dampers and studied its controllability. The controllability in their study was assessed in terms of displacement control, pressure force’s peak value control, width of pressure force platform, and continuity. Hu and co-authors introduced an inertia factor to Herschel-Bulkly model and used an on-off control algorithm to confirm its controllability under high impact loads. Since the recoil cycle is very fast, usually about a few hundred milliseconds, the response time of the MR dampers becomes important and needs to be considered. Hu H. et al did a comprehensive study on the controllability of a MR gun recoil damper12. They first evaluated the response time of a specially designed long-stroke MR gun recoil damper, corresponding to the step signal of the operating current and then, employed three revised control strategies, including the on-off control method, the PID control method, and the adaptive fuzzy control method to confirm the controllability of the MR damper under impact load. Furthermore, Lijie Z. et al did an investigation on modeling, adjustability and controllability of a MR gun recoil damper13. They used a nonlinear model, tested the response time of the MR damping force and finally used the PI control and adaptive algorithms to improve the response time and the tracking ability of the MR damping force. The objectives of the future combat system program call for similar lethality to a current heavy tank but on an extremely lightweight vehicle of nominally twenty tons14. Prior experience with the M551 Sheridan, a light tank first put into production by the United States in 1966, raises concern that firing large caliber armaments from light vehicles may result in unacceptable crew discomfort and vehicular reaction during recoil14. But now, by the advent of the new technologies in military munitions and recoil systems, this trend towards lighter vehicles does not seem that much unachievable. Fire out-of-battery, double recoil, the Davis gun and active recoil mitigation suspension are a few of new integrated technologies being employed. One of the most recent recoil system technologies is Super Rapid Advanced Mortar



System (SRAMS), designed and developed by Singapore Technologies Kinetics (ST Kinetics). A load assist device allows a maximum rate of fire of up to 18 rounds/min and other feature integrated in the design include a special blast diffuser, breech valve mechanism and a bore cooling system15. By employing special blast diffuser and newest technologies, ST kinetics claims to have the world’s least recoil system with a recoil force of less than 14 tonnes when firing a 120mm standard bomb at charge 9, directly measured from the pressure sensors mounted in the barrel. This great achievement enlightens the possibility of mounting such mortars on light wheeled vehicles like HMMWV, more than ever. Since the authors could not find any published research on dynamic analysis and control of integrated mortar-wheeled vehicle systems, along with the urgent need for more vehicle mobility and deployability, and the advent of new low recoil mortar systems, they decided to conduct a study to see if spades can be eliminated from light wheeled vehicles such as a HMMWV.

3 2D HEAVE/PITCH/FORE-AFT VEHICLE MODEL

3.1 System modeling Nowadays many armies are going towards mounting mortars on lighter wheeled vehicles. HMMWV is one of those popular military wheeled vehicles on which numerous mortars have been mounted. Figure 1 shows a typical HMMWV with a mounted SRAMS on it.

Figure 1. HMMWV with mounted SRAMS

For the study of the vehicle response while firing and its control, there should be a mathematical model representative of the integrated mortar-vehicle system. To this end, as the system is considered to be symmetric, a two dimensional model is used rather than a three dimensional vehicle one. The model as shown in figure 2 consists of a 5 degree of freedom vehicle model integrated with a 1 degree of freedom mortar system. Vehicle degrees of freedom are rear and front tire vertical deflections, and chassis heave, pitch and fore-aft motions, designated by , , , and , respectively. Displacement of the recoil mass relative to the barrel is designated by . All other parameters used in figure 2 are described in the nomenclature.



Figure 2. Schematic 2D model of a HMMWV with mounted SRAMS

3.2 Combined mortar-chassis system parameters Mortars and vehicles are usually manufactured by different companies with a variety of physical properties like mass, mass moment of inertia and centre of gravity (cg) location. Therefore, one needs to relate the combined mortar-chassis mass, mass moment of inertia and cg location to those of mortar and chassis. For this purpose, a multi-body model of the mortar-chassis system is needed to relate each separate subsystems physical properties to those of the combined one. Details of this model and the equations relating these properties are not mentioned here. 3.3 System dynamic equations Governing dynamic equations of motion for the model shown in figure 2 can be derived by applying Newton’s second law. After simplification and linearization, the equations in the matrix form will be as follows,

d+ + =Mz Cz Kz r&& & (1) where is the displacement vector defined as:

T[ ]G tr tf ry x y y xθ=z . (2)

In equation (1), , and are mass, stiffness and damping matrices, respectively and are defined in equations (3) to (5):

6 6

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

sin sin cos cos 0 0

c

c

c

tr

tf

r r r c r r

m

I

m

m

m

m m c m h m mα α α α×

=

+

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

M (3)



2 2

6 6

0 sin

( sin cos )

0 0 0 0 cos

0 0 0

0 0 0

0 0 0 0 0

cr cf cr cf cr cf r

cr cf cr cf f hf r hr cr cf r c

hf hr r

cr cr cr tr

cf cf cf tf

r

k k bk ak k k k

bk ak b k a k h k h k bk ak k c h

k k k

k bk k k

k ak k k

k

α

α α

α

×

+ − − − −

− + − − − +

+ −=

− − +

− +

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

K (4)

2 2

6 6

0 sin

( sin cos )

0 0 0 0 cos

0 0 0

0 0 0

0 0 0 0 0

cr cf cr cf cr cf r

cr cf cr cf f hf r hr cr cf r c

hf hr r

cr cr cr tr

cf cf cf tf

r

c c bc ac c c c

bc ac b c a c h c h c bc ac c c h

c c c

c bc c c

c ac c c

c

α

α α

α

×

+ − − − −

− + − − − +

+ −=

− − +

− +

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

C (5).

In equation (1), is the vector of body forces and firing force that can be written as below:

T

d [ 0 0 sin ]c tr tf r rm g m g m g F m g α= +r . (6) It is normally more convenient to transfer differential equations into state space format in order to reduce the order of differentiation. Equation (1) is a set of 6 scalar second order differential equations which can be transformed to 12 first order differential equations if transferred to the state space form. Thus, If equation (1) is rewritten as: -1

d

-1 -1z = -M Cz - M Kz + M r&& & , (7) and state vector is set to:

TT T

12 1× = ⎡ ⎤⎣ ⎦x z z& , (8) then the state equation will be as follows:

= + dx Ax R& . (9) In equation (9), state matrix ( ) and disturbance matrix ( ) are defined as below:

6 6 6 6

12 12 1 1

0× ×

× − −=

− −

⎡ ⎤⎢ ⎥⎣ ⎦

IA

M K M C, (10)

and,

6 6

12 1 d1

0×

× −=⎡ ⎤⎢ ⎥⎣ ⎦

dR rM

. (11)



The output will be the first 6 rows of the state vector (6 degrees of freedom of the system) and their second time derivatives (state accelerations) that can be calculated by making use of the state vector and equation (7). In the coming section, the control strategy used to control the vehicle during firing will be discussed.

4 MR DAMPERS AND CONTROL STRATEGY

4.1 Magneto-Rheological dampers Many armies are already using semi-active dampers as the primary suspension to improve ride and maneuverability of their wheeled military vehicles. Nowadays, MR dampers (MR shock absorbers) are by far the most widely used semi-active dampers. Therefore, in this paper MR dampers are also being considered to not only improve ride comfort and road holding of wheeled military vehicles but also improve the vehicle response during and after cannon or mortar firing. MR dampers use MR fluid as their working medium which is an intelligent fluid with micrometer-sized suspended magnetizable particles that reversibly and almost instantaneously changes its rheological state from liquid to solid in the presence of magnetic field. When external magnetic field is applied, the randomly distributed magnetic particles between the two poles will align themselves along the lines of magnetic flux, forming a chain like structure. This chain-like structure effectively restricts the perpendicular motion of the fluid to the direction of the flux which leads in unique variable viscosity characteristic of MR fluids. Since MR fluid response time to the applied magnetic field is almost instantaneous (of the order of milliseconds), if the magnetic circuit of a MR damper is designed properly, its on-state behavior will be quite controllable. In magneto-rheological fluid devices, there are several modes of operation and they are: flow mode, shear mode, squeeze mode, and lastly the combination of any three modes mentioned above16. Among these modes, MR dampers and shock absorbers usually operate in the flow mode. 4.2 Semi-active control policy In automotive industries, semi-active control policy is usually preferred over active and passive control. Among different control strategies, active control has the best performance but it is very costly and not reliable as compared to its passive and semi-active counterparts. Moreover, semi-active control has most of active control advantages while being low-cost and reliable. One of the most commonly used semi-active control policies is skyhook control which was first introduced in 197317. Skyhook damper is a fictitious damper that fixes the vehicle chassis to an inertial reference in the sky (figure 3). The semi-active skyhook control policy is explained below,

( ) ( )

( )min

, 0

, 0sky b b

MR

b

c y y y y y yc

c y y y

− − ≥=

− <

⎧⎨⎩

& & & & & &

& & & , (12)

where , and are MR damper damping coefficient, skyhook damper damping coefficient, and the minimum MR damper damping coefficient, respectively. and are mass and base velocities as shown in figure 3.



Figure 3. Schematic figure of (a) ideal skyhook and (b) semi-active skyhook configurations

Semi-active skyhook control strategy is utilized in this paper to suppress and control the vehicle motion during and after mortar firing. The continuous skyhook control is applied to both rear and front suspensions and the results are presented in the next section. One should note that the horizontal stiffness and damping have two components; one is constant and resulting from the rubber bushings and other constant sources and the other part is the horizontal portion of the vertical stiffness and damping resulting from deviation of the suspension from its vertical position. The latter part is inherently variable and dependent on the deviation angle of the vertical suspension spring and damper, but for simplicity and avoiding nonlinearity, it is assumed to be a constant portion of the vertical suspension (it will be further addressed in the next section). Therefore, this part of the horizontal damping will also be subjected to the skyhook control as it is inherently a portion of the suspension dampers. 4.3 Method of Simulation In this paper, the intention is to compare HMMWV chassis dynamic response to mortar firing, with and without spades. Modeling a HMMWV vehicle with spades is difficult, particularly since there are different designs of spades, and spade locations. So in this paper, the ideal Skyhook suspension system represents the HMMWV vehicle with spades. The HMMWV vehicle, with passive and semi-active suspensions, is considered as a HMMWV without spades.

5 SIMULATION RESULTS

5.1 Vehicle Description and Properties As mentioned in section 3, a 5 degrees-of-freedom mathematical model is considered for the HMMWV vehicle. The geometric and physical properties of the vehicle chassis are used from those provided by Aardema18 for a standard HMMWV without any shelter or mortar mounted and vehicle suspension and tire properties are adopted from the study conducted by Karakas and his coleagues6, and all are tabulated in Table 1. All the parameters in the table are introduced in the nomenclature.

Table 1. The Vehicle Parameters for the Full Scale Half HMMWV Model Parameter Symbol Value Parameter Symbol Value

1810 kg 9000 N.s.m-1

181 kg 4000 N.s.m-1

181 kg 4000 N.s.m-1

2976 kg.m2 3.3 m 163300 N.m-1 2 m



163300 N.m-1 0.2 m 463800 N.m-1 -0.2 m 463800 N.m-1 0.2 m 9000 N.s.m-1

Horizontal stiffness and damping have two components as discussed in section 4.2. The first part which is resulting from bushings and other constant sources are assumed to be 7 percent of their corresponding passive vertical stiffness and damping. The other component of horizontal stiffness and damping which is due to the deviation of vertical suspension from vertical position is assumed to be equal to 15% of their corresponding vertical values19. In equation (12), the damping coefficient of ideal skyhook dampers ( ) is set to 11000 N.s.m-1, minimum semi-active damping coefficient ( ) is idealized to be 0 and the semi-active skyhook damping coefficients of the suspension dampers are generally variable (continuously varying). Moreover, the friction coefficient between tires and soil is assumed to be 0.720. 5.2 Mortar System Description and Properties The mortar system considered in this paper is a 120 mm smoothbore Super Rapid Advanced Mortar System. The unique design of SRAMS, coupled with other features of its recoil mechanism, has led the SRAMS to achieve an extremely low recoil reading of 13.6 tonnes when firing a 120 mm standard bomb at charge 915. The recoil firing force is modeled as a half sine force with total duration of 50 ms and amplitude of 135.7 kN. The mortar elevation angle is assumed 40 degrees in the simulations unless otherwise specified. Other properties of the mortar are presented in Table 2.

Table 2. The Mortar Parameters for the Full Scale SRAMS Model Parameter Symbol Value Parameter Symbol Value

400 kg 80345 N.m-1 800 kg 0.75 m 2000 kg.m2 1 m

The recoil system of a gun system is essentially a critically damped system to absorb the recoil force21. Therefore, the recoil damping is set so that the local recoil damping ratio is equal to unity. One should note that the properties given here for the mortar system are for a full scale full mortar model, but the properties given for the vehicle are for a full scale half car model. Therefore, once substituting them into the system equations, one should either multiply the vehicle properties by 2 or the mortar properties by 0.5. The geometric properties will not change for this matter. Then with all the vehicle and mortar system properties and specifications along with the equations derived in section 3 and utilizing the semi-active control strategy described in section 4, the simulations are carried out in MATLAB Software and the results are presented in section 5.3. 5.3 Results In this section, the simulation results and some practical issues are presented and discussed. 5.3.1 Chassis heave vibration One of the vehicle motions that might vibrate to extreme values during firing is the heave motion of the vehicle. This can bring about problems both for the vehicle and the crew. Heave displacements of the vehicle for passive, ideal skyhook, and semi-active skyhook dampers are compared in figure 4. All the simulations were run for 5 seconds and all the displacement figures are plotted from the static equilibrium position. Figure 4 shows improvement of semi-active control strategy as compared to the passive suspension, in reducing the vibration amplitude of the heave motion as well as its settling time. In comparison to passive mode, semi-active has a reduction in vibration amplitude by %17, in vibration range (maximum to minimum) by %25, and a reduction in the settling time by %30. The settling time error tolerance in

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this paper is set to 2%. As expected, the ideal skyhook control has the best performance, but as can be seen from the figure, the settling times of semi-active skyhook and ideal skyhook are quite the same.

Figure 4. Time history of vehicle heave in passive, ideal skyhook and semi-active skyhook modes

5.3.2 Chassis pitch vibration and firing accuracy Figure 5 shows the time history of vehicle pitch in different modes. As can be seen from the figure, pitch angle has been increased by removing the spades. However, compared to passive mode, the semi-actively controlled vehicle has a reduction in pitch amplitude by 17%, in range (maximum to minimum) by 32%, and a reduction of 30% in settling time. One can also see from the figure that the semi-active control has a better performance in terms of the settling time even than ideal skyhook. It can also be seen from the figure that the absolute value of vehicle pitch is sufficiently small to be consistent with the assumptions made in simplifying the trigonometric functions in derivation of the system equations.

Figure 5. Time history of vehicle pitch in passive, ideal skyhook and semi-active skyhook modes

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The chassis pitch angle is a very important parameter that not only has an effect on crew comfort but also can affect the firing accuracy. If the momentum velocity of the bomb, leaving the barrel, is designated by , the firing range will be,

20 sin )2(R V gα= , (13)

where R is the range, α is the elevation angle of the mortar from the horizontal plane, and is gravitational acceleration. can be calculated from the firing momentum imparted to the bomb. By assuming a half-sine firing force as mentioned

before, the momentum imparted to the bomb will be,

0 0

sin( ) 2T T

firing r rF dt F t T dt F Tπ π= =∫ ∫ , (14)

where and are firing and recoil forces, respectively. And T is firing duration that is 50 ms. Therefore, if the bomb mass is designated by m, the bomb velocity leaving the barrel i.e. will be,

0 2 rV F T mπ= . (15) Now, one can evaluate the change in the range in terms of a change in the elevation angle by differentiating equation (13) with respect to α. Differentiating equation (13) and substituting from equation (15) yields,

22 (2 ) cos(2 )rdR F T m dg

π α α= . (16)

If the bomb mass is assumed to be 15 kg and the elevation angle to be 4.5⁄ radians (40 degrees), using equation (16), the firing accuracy will be decreased by 13.3 m in the vehicle with passive suspension compared to the vehicle with ideal skyhook suspension (representing the vehicle with spades). This inaccuracy will be improved to 6.7 m if the semi-active control policy is utilized. Effectiveness of the semi-active suspensions in firing accuracy becomes even more evident if the firing takes place at other elevation angles. For example, if the firing elevation angle increases to 3⁄ radians (60 degrees), firing accuracy degrades by 42.7 m in passive mode in comparison to the ideal skyhook mode, while this degradation falls to 19 m with the semi-active suspensions i.e. more than 55% improvement as compared to the passive suspensions. 5.3.3 Tire burst-out and vehicle lift-off One important issue for wheeled vehicles firing mortars is tire burst-out. Outriggers (or spades) are used to prevent tire burst-out, but the spades will make the vehicle stationary during the mortar firing; therefore, easy to be spotted by the enemy, but if spades are removed, tires are more likely to burst out due to the sever shock and excessive load transmitted to them. Tires bursting point is usually characterized by a maximum deflection, a maximum pressure or a maximum load. Therefore, it is crucial to monitor and take into account one of these criteria in order to diagnose and prevent tire burst. In this study, rear and front tire loads are monitored and their time histories are plotted in figures 6 and 7. According to figures 6 and 7, the settling time for rear tires in all three modes is quite the same while for the front tires it has the smallest value for semi-active suspension. Furthermore, in comparison to passive suspension, the semi-active suspension has smaller front tire forces and slightly larger rear tire forces. For both rear and front tires, the vehicle with spades (vehicle with ideal skyhook suspension) has the minimum tire loads. The maximum force in each of the tires in semi-active suspension is about 22 kN for the rear tires and about 18.5 kN for the front tires. The tires usually used in HMMWVs can resist up to 18 kN. Thus, the current tires used in HMMWVs will burst out if the spades are removed. However, by a thorough search in the internet through tire industries, the authors found that there are tires which can resist the 22 kN force generated in tires, in the semi-active suspensions with no spades. Therefore, the problem of tire burst-out in the case of spades removal, can be eliminated by using stronger, more ruggedized tires.

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Figure 6.Time history of rear tire force in passive, ideal skyhook and semi-active skyhook modes

Figure 7. Time history of front tire force in passive, ideal skyhook and semi-active skyhook modes

One should note that by increasing the passive suspension damping coefficients, the similar results as those for semi-active suspension can be achieved. But the problem about increasing passive dampers damping coefficients is that they cannot be decreased when vehicle is no longer firing and is being driven on the road. In this case, large damping in the suspension results in poor ride and comfort quality of the vehicle which will not be an issue for the semi-active suspension since suspension damping can be changed in the ride and firing modes. Thus, using semi-active suspension not only improves ride comfort, road holding and maneuverability of the vehicle but also improves the vehicle response during firing. Another concern during firing is vehicle lift-off that is not desirable and will also result in nonlinear response of the vehicle. The vehicle lift-off can be tracked in terms of tire forces i.e. if they go into negative values (expansion of tires) it means the tires have lifted off the ground. The tire forces shown in figures 6 and 7 are total forces including their initial

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values due to the vehicle weight. Therefore, they can be used to check if the tires have lifted off. As shown in these figures, for both rear and front tires, the tire forces are well above zero so it guarantees that no lift-off occurs for any of passive, ideal skyhook or semi-active suspensions. 5.3.4 Suspension Travel Another issue concerning the suspension system of the vehicle is bottoming-out of the suspension dampers. After a few times they bottom out, the dampers will not function properly. Too see if the dampers bottom out, suspension travel (or rattle space) of the rear and front suspensions of the vehicle is plotted in figures 8 and 9. Suspension travel is the total up and down movement of the suspension with the axle on a level plane. If the suspension travel is larger than the maximum allowed value, the dampers will bottom out. According to figure 8, the suspension travel for the rear suspension is 5.3, 4.2, and 3.2 centimeters for passive, semi-active and ideal skyhook suspensions. Furthermore, according to figure 9, the suspension travel for the front suspension is 4.4, 2.5, and 2.1 centimeters for passive, semi-active and ideal skyhook suspensions. The suspension travels for both rear and front suspensions are in acceptable range, meaning that the dampers will not bottom out. As anticipated, the vehicle with ideal skyhook suspension has smaller suspension travel than passive and semi-active suspensions. Nonetheless, the vehicle with semi-active suspension will have smaller rattle space while firing, by 21% and 43% compared to the vehicle with passive suspension.

Figure 8. Time history of rear suspension travel for passive, ideal skyhook and semi-active suspensions

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Figure 9. Time history of front suspension travel for passive, ideal skyhook and semi-active suspensions

5.3.5 Other practical issues The maximum values of the suspensions damping forces are also important and should be in a feasible range. The maximum damping forces for a single damper of the rear and front suspensions in semi-active mode are about 6600 N and 2100 N, respectively, which can be easily achieved by a properly designed MR damper. Although the main reason for using the MR dampers and controls in the suspension system of the wheeled military vehicle in this paper, was that there are many wheeled military vehicles already using MR dampers as their primary suspensions, there is another significant advantage and a secondary reason for using the MR dampers in the suspension system rather than the recoil system. While the response time of the MR fluid is of the order of milliseconds, the overall response time of the electronic and magnetic circuits and the control system can be much larger. Since the overall response time of the MR damper control system can go higher than the transient excitation duration, 50 ms in this case, utilizing the MR dampers in the recoil system will not be efficient. This is because, before the MR dampers and control system can begin to react, the firing will finish and the firing force will be transmitted to the vehicle chassis without getting controlled efficiently by the MR dampers. However, if the MR dampers are used in the suspension system they will have much more time to react and that is because the transmitted force through the recoil system to the vehicle chassis has larger duration (and smaller amplitude) compared to the direct firing force, which is the main function of the recoil system. In this paper, the force duration has increased by 500% after transmission through the recoil system. This enables the MR dampers and the control system to have sufficient time to react and respond to the excitation and disturbance, and consequently, they will have better performance. The last but not least is hydraulic lock-up problem of the dampers. Fluid valves and nozzles in the dampers are so tiny that if the working fluid is forced to pass through them very fast, it might lock up and even break down the damper. This sometimes occurs if the damper is subjected to high input velocities or forces. In military applications where high shock and firing forces are imparted to the system in a very short time, the lock-up problem of the dampers are more likely to arise. Therefore, the dampers should be especially designed to prevent any hydraulic lock-up problem. One should note that if the dampers are used in the recoil system, this issue becomes more serious and probable, since the dampers will be subjected to higher forces in shorter time compared to the case when they are mounted in the primary suspension system.

6 CONCLUSION

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In this paper, the feasibility of removing spades from wheeled military vehicles during mortar firing has been studied. With the removal of spades, the vehicle becomes more mobile thus more difficult to be spotted by the enemy, but it is anticipated that the removal of the spades may result in excessive chassis vibration, firing inaccuracy, tire burst-out, vehicle lift-off, large suspension travel, and hydraulic lock-up of the shock absorbers. To see how feasible it might be to remove the spades during mortar firing, a dynamic model of a HMMWV plus a mortar has been developed, using MR-dampers as primary suspensions to control chassis motions. Two control strategies, namely ideal skyhook and semi-active skyhook policies were employed for the MR dampers. The ideal skyhook control policy was chosen as an approximate representative of a HMMWV with spades. By removing the spades, the vehicle heave and pitch motions were increased in both passive and semi-active suspensions as compared to the vehicle with ideal skyhook suspension (vehicle with spades). Moreover, the firing accuracy of the vehicle was degraded by spade removal in passive and semi-active suspensions. However, the simulation results show that the semi-active suspension has better performance than the passive suspension, in terms of vehicle vibration response and firing accuracy. Furthermore, there was no vehicle lift-off in either passive or semi-active suspensions. Simulation results show that the required MR damper damping forces to control chassis motion during firing are in a feasible range. Suspension travel of the dampers was also monitored and there was no excessive suspension travel that could lead to dampers bottoming out. Furthermore, the hydraulic lock-up issues of the dampers can be easily prevented by a proper design of the MR-dampers. Simulation results indicate that if spades are removed from the existing HMMWVs with stock tires, the tires will burst. However, the authors found other ruggedized tires capable of handling the maximum tire forces occurred in the semi-actively controlled dampers and, thus this problem can be solved by choosing appropriate tires. Simulation results indicate that removal of the spades is feasible. This achievement consequently, reduces the vehicle weight and the time duration for shoot and scoot, thus, results in more mobility for the HMMWV. In summary, use of MR dampers as primary suspensions not only provides ride comfort, road holding and maneuverability for the HMMWV during normal driving but also removes the need for spades.

ACKNOWLEDGMENTS The authors would like to gratefully acknowledge the financial support of Singapore Technologies Kinetics (ST Kinetics).

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